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An application of the theorem on Sums to viscosity solutions of degenerate fully nonlinear equations

Part of: Close-to-elliptic equations and systems Representations of solutions Partial differential equations

Published online by Cambridge University Press:  26 January 2019

Fausto Ferrari
Fausto Ferrari*
Affiliation:
Dipartimento di Matematica dell'Università di Bologna, Piazza di Porta S. Donato, 5, Bologna40126, Italy (fausto.ferrari@unibo.it)
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Abstract

We prove Hölder continuous regularity of bounded, uniformly continuous, viscosity solutions of degenerate fully nonlinear equations defined in all of ℝn space. In particular, the result applies also to some operators in Carnot groups.

Keywords

Degenerate elliptic operatorsnonlinear elliptic operatorscarnot groupsviscosity solutionstheorem on sumsHölder regularity

MSC classification

Primary: 35D40: Viscosity solutions
Secondary: 35B65: Smoothness and regularity of solutions 35H20: Subelliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 2 , April 2020 , pp. 975 - 992
Copyright
Copyright © Royal Society of Edinburgh 2019

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